Tag Archives: multiplication

Problem-solving with pigs: Start at the end

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📖Standard

CCSS.MATH.PRACTICE.MP4 Model with mathematics.

CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.

⏰ Time

60-75 minutes

📃 Summary

This cross-curricular lesson includes activities and instruction in agricultural science and math. Students begin by watching a video and learning about pig farms. After making their own pig barn, they watch two short videos about solving math problems. This information is then applied to solve problems during a presentation on math around the pig farm. Students end playing one of the Making Camp games to reinforce skills and knowledge.

📲 Technology Required

If teaching in person, the teacher will need a computer and projector or smart board to show the videos, or students can be given the links to watch on their own devices. Students will need a PC, Mac or Chromebook or tablet. Making Camp Premium, Making Camp Lakota and Making Dakota are all playable on any web browser on those devices.

📚 Lesson

This lesson starts with resources from National Ag in the Classroom

Virtual tour of pig farms

Virtual Field Trip to Ohio Pig Farms

Make a Pig Barn

This activity requires a few supplies but it is probably things you have lying around and your students will probably enjoy it.

Business-size envelopes, 4 per group
Paper towel, 1 per group
Scissors
Scotch tape

OPTIONAL

Markers
Toilet paper rolls, 2 per group
Drinking straws, 2 per group (cut into 8 equal pieces)
8.5″ x 11″ white paper, 1 per group (cut in half)
Extra paper for making fencing, pipes, feed troughs, etc. (optional)

Instructions

Use the following instructions to model for the students how to create the barn:

Barn: Cut an oval hole in one envelope, making a large side window for the barn. This window provides the proper ventilation for the pigs.
Cut the paper towel in half and tape it onto the top of the window for the curtain.
Cut another envelope in half for the ends of the barn.
Tape the ends of the barn to the “sides of the barn” envelopes, one of which has the hole for the window and paper towel curtain, so that you have four sides, or a rectangle.
Use the final envelope to create a roof by creasing it in half lengthwise and attaching it with tape to the top of the rectangle.
Food Storage: Tape four straws, or legs, to each toilet paper roll so that the structures will stand on the legs.
Use a half piece of paper, and make a cone shape by twisting and taping the ends. Tape the cone shape on the end of the toilet paper roll without the straw legs.
Use the other half piece of paper to make another smaller cone shape and tape it between the straw legs on the other end of the toilet paper roll.

If you’d like, you or your students can watch the instructions here. You can also assign this video for students learning at home to watch so they know how to make the barn. The plus is that just about every house will have every single one of these items except possibly the straws.

Optional additional science and language arts content

This link to the National Ag in the Classroom lesson has more information on pigs and pig farming, including some of the vocabulary used in the math lesson as well as a discussion of the ways farmers care for animals. I highly recommend checking it out.

Watch a video on operations key words

Trust me, this does come back to pig farming!

Students watch this video on operations keywords. This two-minute video has been watched over 14,000 times, which gives some indication of how useful students and teacher find the concept of looking at the words in a problem to decide which operation to use.

Watch a video on problem-solving – Start at the end

This 3 1/2 minute video explains that the end of the word problem is where you usually will find the question you are expected to solve. It includes one easy and one harder example, as well as a couple of useful tips.

Start at the End

Give a presentation

This 34-slide deck on problem-solving reinforces the information in the two math videos and gives students three problems of increasing difficulty where they have to start at the end, all centered around Laura’s pig farm.

Play a game

Now that students have been introduced to problem-solving with multiplication and division word problems, it’s time to play a game and reinforce those skills. Which game depends on what you feel your students need most. There is overlap among the games as each includes some review.

Making Camp Premium – focuses primarily on multiplication of one- and two-digit numbers. Also includes division with one-digit divisors. The content is taught in the context of Ojibwe history and culture.

Making Camp Lakota – focuses primarily on division with one-digit divisors. Also includes multiplication of one- and two-digit numbers. The content is taught in the context of Lakota history and culture.

Making Camp Dakota – focuses primarily on division of three-digit numbers with one- and two-digit divisors. Also includes multiplication of one- and two-digit numbers and division with one-digit divisors. The content is taught in the context of Lakota history and culture.

Assessment

Assessments are built into the presentation, as teachers can have students submit their answers in writing or in a Google chat prior to giving the answers during the presentation. Teachers can also see which standards students have attempted and how many problems they have answered correctly in the Making Camp teacher reports.

Related lesson : Problem-solving Two ways

As the title suggests, this lesson introduces students to two other problme-solving strategies. They watch a video on visualization, then solve a problem that asks them to visualize. After watching a video on building a model, students build and/or draw their own model of a multiplication problem or property.

Multiplication Terms

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📖Standard

CCSS.Math.Content.3.OA.B.5 Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.)

CCSS.MATH.CONTENT.3.OA.A.1
Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.

⏰ TIME

40 minutes

📲TECHNOLOGY REQUIRED

In class:

Printer to print cards. Computer with projector in classroom to watch video. Access to computers or tablets to play games.Students can also play on phones.

Link for flash cards if you don’t have two-sided printing. Students cut and fold the cards.

Link for flash cards if you DO have two-sided printing. Just print out one sheet and have students cut out the cards.
Hint: If using this as a center activity or for multiple classes, teachers may wish to make a few sets of cards and laminate them.

Remote:

Computer with Internet access to view flash cards, watch video and play games.

📃 SUMMARY

Students watch a video on multiplication terms then review terms with flash cards. Students quiz each other with flash cards. The lesson closes with practicing multiplication and division by playing Making Camp Premium.

📚 Lesson

Watch video

Learn Multiplication Terms with Ms. Sancjhez

Perhaps you know the definition of a product and a factor, but what about the distributive property of multiplication? Have you ever thought about the Identity Property as a mirror or the Zero Property of Multiplication occurring because zero is a number that won’t share the spotlight? Learn these and more with Ms. Sanchez.

Make the Cards

I strongly recommend having students make their own cards. It saves work for the teacher, it is one more opportunity for students to see the material and some students learn better when physically engaged.

If you will be using printed flash cards, there are two downloadable PDFs.

If you can print two-sided, you can just print out these sheets. They can cut the cards out with scissors, with the term on the front and the definition on the back.

If your printer doesn’t print two-sided, you’ll find it easier to use these sheets because the definition of each term is next to it. The student can cut between cards and then bend in the middle of the paper to have term on the front and definition on the back.

Present multiplication terms to students (Optional)

Teachers may wish to present multiplication terms using this Google slides deck. Copy to your own Google drive and edit to add additional cards or explanation.

Review multiplication terms flash cards

Students review math cards individually.

Students can review using printed cards or review cards in a Google slides presentation shared with students . This activity should take 5-10 minutes.

Students review with classmates

After reviewing individually, students take 5 minutes to pair up and quiz their classmates. Students should take turns giving a term and asking for the definition. Students learning remotely can pair up with a classmate and take turns using the Google slides presentation to quiz one another.

Play a game

Students play the Making Camp Premium game to practice multiplication and division.

Assessment

Making Camp Premium offers Data and Reports for teachers to access after students are finished playing. If you are remote teaching students experiencing low internet connectivity students can play offline but the data will not be transmitted to show their progress.

Watch out for blood-sucking fishes!

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📖STANDARD

CCSS.ELA-LITERACY.RI.5.4 Determine the meaning of general academic and domain-specific words and phrases in a text relevant to a grade 5 topic or subject area.

CCSS.MATH.CONTENT.5.NBT.A.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

CCSS.MATH.CONTENT.5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm.

⏰TIME

40 minutes

📲TECHNOLOGY REQUIRED

Either a project or smart board connected to the computer will be required to view presentation and videos in class or students will need a computer to watch during a web meeting. The game can be played on any computer or tablet.

📃SUMMARY

This lesson introduces new science vocabulary words, teaches about indigenous and invasive species and includes a couple of math problems showing how quickly invasive species multiply. It concludes with students playing the Making Camp Dakota: Past and Present game.

📚LESSON

Watch the Mouths to Feed Video

Invasive Species Giant Insect!

This one-minute video is a little silly with a giant insect but it is a good starter for the lesson to spark student interest.

Give a presentation on indigenous and invasive species

This Google slides presentation introduces the concepts of indigenous and invasive species. It also provides geography information on the Great Plains and Great Lakes as well as a couple of math problems computing how quickly one fly can turn into 5,000.

This content can be assigned to students as reading, but we recommend the teacher present as a mini-lecture first, if possible, and include the reading for students to review.

Watch video Seven Ways to Leave Hungry Pests Behind

We recommend assigning students to write down any words in the video that they don’t recognize.

Play Making Camp Dakota: Past and Present

Have students access the Games Portal for Kids to play Making Camp Dakota: Past and Present. If you want sections specific to this lesson in indigenous plants and animals, have them select the two icons below.

In the LIFE section of Making Camp Dakota: Past and Present, select this icon to learn about how indigenous people used herbs.

In the NUMBERS section, select this icon to learn about buffalo hunting.

As an added bonus, the buffalo section ends with a question on division of three digit numbers.

Buffalo hunt long division problem from Making Camp Dakota — Buffalo Hunt Division – from Making Camp Dakota

Optional: Lesson challenges and extension

National Ag in the Classroom has four, related lessons at the sixth to eighth-grade level on invasive species. Some of the readings may be above the grade level, but they recommend “jigsaw reading” where each student in a group takes a piece of a reading, then explains that paragraph or two to the rest of the class.

If your students are interested in invasive species, or you want some students to have more of a challenge, we recommend checking out this resource.

Assessment

In-class formative assessment occurs when asking students to answer math problems during the lesson. Students learning remotely can post answers in chat. Students in a classroom can hold up a piece of paper with their answer, allowing the teacher to check understanding at a glance.

Completion and accuracy of the responses in Making Camp Dakota can be checked in the data reports.

Two-Digit Multiplication and Estimation

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📖Standard

CCSS.MATH.CONTENT.4.NBT.B.5 – Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations.

⏰Time

35- 45 minutes

📲Technology Required

Computer with a projector, Smartboard or other device for your class to watch videos

NOTE: You’ll also need 20 math problems: 3-digit numbers multiplied by a 2-digit number. You can use what you already have, use the worksheet provided or use the Multiplication Worksheet Generator to make your own worksheet.

📃Lesson Summary

Students practice multiplication for a few problems, watch a video on using estimation to solve problems, hear a brief presentation from their teacher, solve more practice problems, watch a second video and practice more problems. They end the lesson with a game and a discussion of which strategies proved most useful.

📚Lesson Plan

Start with multiplication problems

Have the students solve 3 to 5 problems.

NOTE: This lesson requires a total of 9 to 15 multiplication problems. This worksheet has 24 problems multiplying a three-digit numbers by a two-digit number. Teachers can assign any selection of these problems or use their own. We give the students a worksheet of 24 problems and tell them to pick any ones they want to solve. Of course, teachers should do whatever works for them.

A PDF of the answers to the multiplication problems can be found here.

Watch a video

This 3-minute video explains multiplication of 2-digit and 3-digit numbers

This video explains steps in long multiplication, with examples and a reality check.

Discuss the video

Use this Google slides presentation for a short discussion of the video and how to apply the information learned about estimation and long multiplication.

Practice multiplying 2-digit and 3-digit numbers again

Now that students have had a chance to watch and discuss the video showing long multiplication, step by step, it’s time for them to practice again. They have 10 minutes to complete another 3 to 5 math problems.

Watch another video to review the steps

Now that students have watched one video and practiced their skills with a few problems they watch a second video to reinforce those steps.

Practice multiplying 2-digit and 3-digit numbers again

Peer-grading (optional)

You may wish to share the answer key with students and have them grade their own or their peer’s problems.

Discussion

As a class, discuss strategies for solving problems, including doing a reality check, estimation and breaking problems into smaller problems. Ask students which strategies worked best for them.

Play a Game

Both Spirit Lake: The Game and Making Camp Dakota (released in February, 2021) teach multiplication of two- and three-digit numbers.

Assessment

In addition to grading all of the multiplication problems, remember that you can always see your students’ performance on the problems in Making Camp and Spirit Lake by accessing the reports page. You will need to enter the password you received during training.

10 Minute Mini-Lesson: Rabbit Stew & Multiplication

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📖Standard Standards

CCSS.MATH.CONTENT.3.OA.A.4-Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

CCSS.MATH.CONTENT.3.OA.C.7– Fluently multiply and divide within 100

⏰ Time

10 Minutes

📲 Technology Required

Device with web-browser – Chromebook, laptop or desktop computer, phone or tablet

📃 Summary

Students learn about what foods the Ojibwe people ate and how their diet changed when they were forced on to the reservation. They play a multiplication tic-tac-toe to snare rabbits and spend the points earned in the game to outfit their wigwam.

📚 Lesson

1. Watch a one-minute video on rabbit stew

Narrated by Deb Gourneau, of Turtle Mountain, this video explains the importance of rabbit stew in helping people survive when food was scarce.

2. Play Rabbit Tic-Tac-Toe in Making Camp Premium

Remember, clicking on the link with the boxes in the bottom left corner will always take you to the choices page.

Click on the box with the rabbit to play a tic-tac-toe game in Making Camp. Each correct multiplication problem snares a rabbit. Incorrect problems leave an empty snare.
When you win this game, there will be an arrow to go back to the numbers page.

3. Play a Matching Game to earn more points

Click on the box with the buffalo to match multiplication problems with their answers.

4. Learn what else was part of the Ojibwe diet

Now that you have 4 more points, go back to the wigwam and if you have not already traded for these, select the fish, deer hide or parfleche to see what else the Ojibwe would eat. Click on each of these items in your wigwam to learn more about it.

Assessment

Remember that you can always see your students’ performance on the problems in Making Camp Premium by accessing the reports page. You will need to enter the password you received during training.

State Standards

Minnesota Math Standard 3.2.2.2 – Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true.

Minnesota Math Standard 4.1.1.1 – Demonstrate fluency with multiplication and division facts.

Minnesota History Substrand 2, Standard 3. Historical events have multiple causes and can lead to varied and unintended outcomes.

Using estimation in multiplying two-digit numbers

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📖 Standards

CCSS.MATH.CONTENT.4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations.

CCSS.MATH.CONTENT.4.OA.A.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operation … Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

⏰ Time

This lesson takes 40 minutes to an hour, depending on how long you allot your students to complete each of the 4 problem sets and whether you have students play the game.

📲 Technology Required

Computer with a projector, Smartboard or other device for your class to watch videos or videos can be shared in Google meet or other application for remote learning. Spirit Lake: The Game can be downloaded and played on Windows or Mac computers. An iPad version will be available by Fall 2021. Schools that are part of the Growing Math project or who have a 7 Generation Games site license will have access to all of these games for students to use at home or school.

Optional Recommended Resource

Use resources like the Helping Math Multiplication Worksheet Generator to make your own worksheet. Their worksheets look very much like this one on multiplication of two-digit numbers with Easter egg examples, except with many more activities in each worksheet. Note that the link will require you to register for a free download. Registration takes about 1 minute. You’ll then receive a link to download over 100 free worksheets on math topics from addition to rational numbers. Another resource we like is the Lizard Point math worksheet generator. Both will print the worksheets as well as the answer key. Note that sites using PRINT TO Google Drive may have that feature disabled after December, 2020. However, you can still from the PRINT menu select SAVE AS PDF, download a file as PDF and then upload it to your Google Drive. The Growing Math project has no affiliation with Helping Math or Lizard Point.

📃 Summary

You’ll need 20 math problems multiplying two-digit numbers. You can use math problems you already have or use one of the online worksheet generators. Based on research showing the effectiveness of distributed practice – that is, practicing a skill for more, shorter periods rather than one long session – we have students solve a few problems at a time, with videos in between. The lesson begins with a brief explanation of multiplying two digit numbers, followed by students solving 3-5 problems multiplying two-digit numbers. Students then watch a 3-minute video that works an example of multiplying a three-digit number by a two-digit number. They then solve 3-5 more problems, followed by another video, then more problems. We recommend giving a time frame – say, 7-10 minutes – to solve the problems rather than set number of problems because this allows you to begin and end each section of the lesson with all of the students at once.

📚 Lesson Plan

1. Introduction to Multiplying Two-digit Numbers

Begin with an example from Helping with Math, that gives an explanation of multiplication and a variety of types of problems. Then, have the students try to solve 3 to 5 problems. You can use those included in the Google slides linked or create your own.

2. Video : Multiplication and Estimation

Estimation is one of the most practical math skills!

There are a lot of math concepts that I use regularly when writing software or computing statistics in my day job. The one skill I use all the time is estimation. (I can tell you that the ability to accurately estimate an answer is not universal.)

Example 1: Long multiplication using “math reality checks.”

In the problem in the video above, we start out by multiplying 892 x 11, using the fact that any number multiplied by 10 is just that number with an added zero. To test our answer, we round 892 to 900 and can estimate that our answer should be near to – and less than – 9,900.

Let’s say you type the wrong number in your phone, hitting the 6 instead of the 9, since these two are pretty close and you have big fingers. Now your answer is 7,612. If you have a good grasp of estimation and multiplication, that is clearly wrong. If you’re computing how much money you need to charge a customer based on the 892 hours you expect to work at $11.00 per hour, you have just lost out on over $2,000!

3. More multiplication problems

Now that you have had a little practice and a little instruction, students solve another 3-5 problems.

4. Video : Multiplication and Estimation

This video works through a problem multiplying a 3 -digit number by a two-digit number . It also gives a strategy for solving difficult problems. That is, break the problem into smaller, easier problems.

Video 2: Use addition to solve a multiplication problem.

Here, because the last digit of one number is 7 and of the other number is 2, you know that 7 x 2 = 14. So, whatever else your answer is, it has to end in a 4.

5. Follow up to the video

As a math teacher, I heard approximately 4,897,234 times from students:

WHY do I have to do so many problems of the same type?
– Almost every student I ever taught math

Explain to students that all of those facts learned, like 2 x 7 =1 4 are the basis for the commutative property of multiplication, reducing numbers to lowest terms, or solving equations by multiplying or dividing both sides by a constant, and more. You need a BASE to work from, problems that can be examples.

The fact is that the more experience you have with numbers, the more problems you solve. The more problems solved, the easier it gets.

6. Finish off by a few more math problems

Now that you’ve watched another video, it’s time for the last set of math problems.

7. Optional – Game Play

Students can Spirit Lake: The Game . Multiplying two- and three-digit numbers comes up in Level 4. We recommend allowing students to play for 15-30 minutes each session. This gives them enough time to get started but not enough time to get bored.

Assessment

Answers to the 12 -20 math problems completed by the student provide one assessment. A second assessment is in the reports for the Spirit Lake game, which show whether students answered correctly the problems in Level 4, whether they read the hint before answering the problem, and whether they were correct on the first try or had to attempt the problem more than once.

State Standards

Minnesota Math Standard 4.1.1.3 – Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms.

Minnesota Math Standard 5.1.1.4 – Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results.

Multiplying one-digit numbers: 0 to 5

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📖 Standards

CCSS.MATH.CONTENT.3.OA.A.1 – Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each.

CCSS.MATH.CONTENT.3.OA.A.3– Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.

CCSS.MATH.CONTENT.3.OA.A.4– Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

CCSS.MATH.CONTENT.3.OA.C.7– Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

⏰ Time

Each lesson will require 20-30 minutes. With the five lesson plans, total time is approximately 2 to 2 1/2 hours spread over one to two weeks.

📲 Technology Required

Making Camp Premium plays in any browser, so, of course, on Chromebooks. It can also be downloaded on phones or tablets and played offline by students who have limited Internet access. The teacher will need a computer, for showing to students learning from home, and a projector if showing videos in the classroom. If the classroom does not have access to a projector, the videos can be skipped.

📃 Summary

Our single-digit multiplication series is for Grade 3. The lesson plans with PDF links for printing and Google slide presentations are provided below. If you need to go back to basics, visit ‘Multiplication as Repeated Addition.’ While it may be tempting to do all lessons in one week, we have found it works better to spread this over a two-to three-week unit.

Students use visual drawings, manipulatives, and a number line to learn multiplication of one-digit numbers, coupled with their verbal explanations.
Students will create number sentences independently and with a partner.
Learning and memorizing multiplication patterns will improve later understanding of division.
Determine the unknown whole number in a multiplication equation relating three whole numbers.
Optional Brain Power activities have students write their own word problems.
Students play games that reinforce memory and apply multiplication in word problems.

📚 Lesson Plans

Learning from home / hybrid learning tip

Several lessons include an activity, “Work with a partner. Take turns creating your own number sentences and solving them.” This can be modified in three ways:

In a hybrid class, where students come in half of the days, have students leave the number sentences to be solved by the other half the following day. Of course, students can also do the activity with other students in their class that day.
If students are learning from home using Zoom or Google Meet, they can post their number sentences in the chat for other students to solve.
Students at home can include their number sentences in homework they return either in packets or electronically and receive number sentences submitted by other students returned in the same format (homework packets, email, etc.)

Lesson 1 – Multiplying by 0 or 1

Tell students that this week they are going to learn how to multiply numbers from 0 to 5. On Friday, they will be able to play games that use multiplication. They can watch the video below to see what’s coming up. It is deliberately a quick view to get students curious and motivated to get to the games coming up.

Students learn the meaning of a number times zero, or zero times a number, both as regards to equal-size groups and number line jumps. Today’s lesson starts with a Google Slides presentation that shows how multiplication of 0 and 1 works. Feel free to modify the slides to provide more explanation as needed by your students.